Problem: Simplify the following expression: $t = \dfrac{r^2 + 3r + 2}{r + 1} $
Answer: First factor the polynomial in the numerator. $ r^2 + 3r + 2 = (r + 1)(r + 2) $ So we can rewrite the expression as: $t = \dfrac{(r + 1)(r + 2)}{r + 1} $ We can divide the numerator and denominator by $(r + 1)$ on condition that $r \neq -1$ Therefore $t = r + 2; r \neq -1$